SUMMARY
The rectangular weirs with and without lateral contraction are theoretically examined, more particularly their discharge coefficient. Under the realistic assumption of a critical state at the location of the weir, the application of the energy equation between two judiciously chosen sections, while taking into account the effect of the approaching flow velocity, leads to a third degree equation. The analytical solution of the equation shows that the discharge coefficient is a function of both the relative height of the weir and the rate of contraction. This is what the relationships drawn from the experiment reveal. It was easy to deduce the discharge coefficient of the rectangular weir without lateral contraction by writing that the contraction coefficient is equal to unity. The theoretical relationship of the discharge coefficient is compared to the experimental tests abstracted from the literature and is corrected consequently to be in conformity. Also, a comparison is made with the recognized experimental relationships proposed by some research workers and good agreement is observed.